Multipeakons and a theorem of Stieltjes

Abstract

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.

6 pages

Cited by in corpus (56)

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• Inverse Scattering Transform for the Camassa-Holm equation
• Multi-peakon solutions of the Degasperis-Procesi equation
• The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's of Shallow Water and Dym Type
• The Cauchy two-matrix model
• A synthetical two-component model with peakon solutions
• Bäcklund transformations for the Camassa-Holm equation
• A new two-component integrable system with peakon solutions
• Generalised Fourier transform for the Camassa-Holm hierarchy
• A general family of multi-peakon equations and their properties
• Lax integrability and the peakon problem for the modified Camassa-Holm equation
• Poisson structure and Action-Angle variables for the Camassa-Holm equation
• Dynamics of interlacing peakons (and shockpeakons) in the Geng-Xue equation
• Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
• Smooth and Peaked Solitons of the CH equation
• A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions
• Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
• Conformal Properties and Baecklund Transform for the Associated Camassa-Holm Equation
• A view of the peakon world through the lens of approximation theory
• The general peakon-antipeakon solution for the Camassa-Holm equation
• The inverse spectral problem for the discrete cubic string
• An Application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
• Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
• Peakons and Cauchy Biorthogonal Polynomials
• Cuspons, peakons and regular gap solitons between three dispersion curves
• New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation
• On isospectral deformations of an inhomogeneous string
• Generalised Fourier Transform and Perturbations to Soliton Equations
• Equations of the Camassa-Holm Hierarchy
• Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I
• Stability of solitary waves of a generalized two-component Camassa-Holm system
• Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation
• Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice
• Peakons arising as particle paths beneath small-amplitude water waves
• Ghostpeakons and Characteristic Curves for the Camassa-Holm, Degasperis-Procesi and Novikov Equations
• Isospectral flows for the inhomogeneous string density problem
• Integrable negative flows of the Heisenberg ferromagnet equation hierarchy
• Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing
• Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity
• Shock creation and Painlevé property of colliding peakons in the Degasperis-Procesi Equation
• Unique Continuation Properties for solutions to the Camassa-Holm equation and other non-local equations
• Stability of peakons for the generalized modified Camassa-Holm equation
• An integrable semi-discrete Degasperis-Procesi equation
• Analysis of singular solutions for two nonlinear wave equations
• Multipeakons and the Classical Moment Problem
• Convergence of the dispersion Camassa-Holm N-Soliton
• The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem
• Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space
• Similarity reductions of peakon equations: the $b$-family
• Conformal and geometric properties of the Camassa-Holm hierarchy
• The blow-up phenomena and exponential decay of solutions for a three-component Camassa-Holm equations
• The Canada Day Theorem
• Algebro-Geometric Solutions of the Camassa--Holm hierarchy
• Cauchy Biorthogonal Polynomials
• Attractors for the viscous Camassa-Holm equation
• A reciprocal transformation for a 3-component Camassa-Holm type system